diff --git a/theories/fin_maps.v b/theories/fin_maps.v
index b720debf960a99d1c7d52e3f2947fed49079af20..a30f41b07302dee829e696855d5f75e661ae30ca 100644
--- a/theories/fin_maps.v
+++ b/theories/fin_maps.v
@@ -1380,8 +1380,8 @@ Section map_filter_misc.
   Lemma map_filter_empty' m :
     map_Forall (λ k v, ¬ P (k,v)) m → filter P m = ∅.
   Proof.
-    intros HA. apply map_eq. intros i'. rewrite lookup_empty.
-    apply map_filter_lookup_None. right. apply HA.
+    intros HA. apply map_empty. intros i'.
+    apply map_filter_lookup_None. right. by apply HA.
   Qed.
 
   Lemma map_filter_empty : filter P (∅ : M A) = ∅.